Magnetic resonance imaging (MRI) methods have been developed for industrial, medical, and research applications. These methods are based on situating a specimen in a strong static magnetic field (B0), and magnetically manipulating and interrogating nuclear spins. Detected signals can be based on, for example, rotating spins that are aligned with B0 to have spins that are perpendicular to B0, and then detecting the return of the spins into alignment with B0. In other examples, various radio-frequency (RF) pulses and pulse sequences are used to prepare the spins for interrogation. Such sequences can be used to produce spin echoes, stimulated echoes, gradient echoes and to detect the motion of spins. Typically a series of pulses and pulse sequences are applied so that an image can be obtained based on a series of planar sections or “slices.”
In most MR image acquisitions, a gradient magnetic field G is applied so that the Larmor frequency ω of sample spins is spatially varying asω({right arrow over (r)})=γB0 +γ{right arrow over (G)}·{right arrow over (r)}.Total signal amplitude S(t) can then be written as in the form of a Fourier transformation such thatS(t)=∫∫∫ρ(r)exp[iγ{right arrow over (G)}·{right arrow over (r)}t]dr.For convenience, this signal amplitude is commonly expressed in terms of a reciprocal space vector {right arrow over (k)}=(2π)−1γ{right arrow over (G)}t. Using this reciprocal space vector, the signal amplitude S(t) is the Fourier transform of the spin density ρ(r):S(k)=∫∫∫ρ(r)exp[i2π{right arrow over (k)}·{right arrow over (r)}]dr.Thus, obtaining an estimate of the desired signal ρ(r) requires acquiring signals associated with a variety of k values or “sampling” of k-space.
In so-called “phase contrast” MRI, spin motion can be measured non-invasively. Phase contrast MR uses the first gradient moment of bipolar gradients to encode the motion of the nuclear spins into the phase of the magnetization, and ultimately, into image phase. To eliminate the non-motion related phase variations from radiofrequency receiver coils, two images are acquired with different first gradient moments. The phase difference between the two acquired images is proportional to the velocity of the spins in the imaged object. Phase contrast MRI can be used to, for example, image blood flow in vivo, or in other applications in which spin motion in a specimen is of interest. Unfortunately, such phase contrast MRI requires acquisition of two images, and therefore total signal acquisition time is twice that required in anatomical imaging which can limit the spatial or temporal resolution of acquired images. Accordingly, improved methods and apparatus for acquisition of images and data for phase contrast MRI are needed.